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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2018 Volume 476, Pages 111–124 (Mi znsl6727)

This article is cited in 2 papers

Local smooth conjugations of the Frobenius endomorphisms

V. S. Kalnitsky, A. N. Petrov

Saint Petersburg State University, Saint Petersburg, Russia

Abstract: In the paper, one of the generalizations of the Böttcher equation is considered. It turned out that the parametrized Poisson integral, as a function of its parameters, satisfies an equation of the type described. The structure theorem for splitting maps of the Frobenius endomorphism in a ring and in an algebra over it is proved. The real field case is considered. The generalized Böttcher equation is solved for classical two-dimensional algebras and for the Poisson algebra.

Key words and phrases: the Frobenius endomorphism, splitting operator, the generalized Böttcher equation.

UDC: 517.965

Received: 04.06.2018



© Steklov Math. Inst. of RAS, 2024